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C₂×#2794 #52239

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

883 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(12,15)(13,17)(19,20,23,25)(21,22,24,26);(4,7)(8,9)(11,12,14,15)(13,18,17,16)(19,21)(20,22)(23,24)(25,26);(3,5,6,10)(4,8,7,9)(19,22)(20,24)(21,25)(23,26);(3,4)(5,8)(6,7)(9,10)(11,13,14,17)(12,16,15,18)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45227);